The price of anarchy in closed-loop supply chains

This paper measures the worst-case efficiency of price-only contracts in closed-loop supply chains (CLSCs) with the price of anarchy (PoA). We model a single-period Stackelberg game in which a manufacturer sells new products to a retailer and collects used products with exogenous retail price and collection price via three alternative reverse channels: (a) the manufacturer collects directly from customers, (b) the retailer collects for the manufacturer, and (c) a third party is awarded a collection subcontract from the manufacturer. We carry out a comprehensive investigation under push-pull configurations to observe how reverse channel structures with different gaming sequences of CLSC members influence the worst-case performance when the demand distribution is over the set of increasing generalized failure rate distributions. From our PoA analysis, we find that the pull system does not always outperform the push system, especially when the retailer is the leader, in contrast to the results for forward supply chains. While the PoA of the push system is dramatically sensitive to the quality condition of used products, the pull system has a constant efficiency loss that is independent of the quality condition. Instead, the PoA of the pull system solely changes with the gaming sequence of the manufacturer. We also find that manufacturer's direct collection is a better reverse channel choice compared to retailer's collection. Additional managerial insights are summarized for discussion.